What research could/should be done with an unlimited budget?

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shipoftheseus
Science fiction often (really, almost always) deals with the possibilities of scientific research that is not constrained by funding requirements. I was inspired to pursue my career from reading and watching these stories, and of course learned a long time ago that this is not realistic. Having recently begun a PhD in Materials Science I have become even more aware of how money limits the directions in which research can move. Granted, quite a few discoveries have been made in an attempt to get around budgetary limitations or a lack of ideal materials, but I think it is interesting to speculate about what could be done in our Universities and laboratories if costs were negligible to non-existent (but everything was grounded in our current understanding of reality, i.e. no speculative physics).

Some ideas:
Fusion energy
Massive solar arrays
Spaceflights (Mars and beyond)
Truly huge supercomputers (although the speed of light/information throughout the computer could be a real problem)
Space elevators
Space catapults

I am hoping that some people with academic or laboratory research careers under their belts can contribute stories about funding limiting their work. I still have a little idealism and I hope I can be inspired!
 
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Research budget limitations are a functional reality.
There is no way to get around this.

Even "black" projects are budget constrained(possibly modified with "success" but still constrained.

As such, in my opinion, an "unlimited" budget is non-sensical.

Speculation with an unlimted budget serves no useful purpose, as there will always be a budget cap, modified or not.
 
While there are many novel ideas as to which this inexhaustible funding could be used, I think its most attractive point would be its impact on popular science.

The space race begot a generation of scientists - we need another mammoth scale project to do the same.